Katrina draws a regular n-sided polygon. What is the value of n?

We need to determine the value of n in a regular n-sided polygon, that is, we need to determine the number of sides of this regular polygon.

Statement One Alone:

One internal angle of the polygon is 108 degrees.

Since we have a formula for the sum of the measures of all the interior angles of a polygon, and since all the angles of a regular polygon are equal, knowing the measure of one interior angle of a regular polygon is sufficed to determine the number of sides of the polygon. Statement one alone is sufficient. (Note: here n = 5, but we will leave the readers to verify it.)

Statement Two Alone:

The sum of all the side lengths is 120.

This means the perimeter is 120. However, without any further information, knowing the perimeter of a regular polygon doesn’t allow us to determine the number of sides of the polygon. Statement two alone is not sufficient.

Answer: A

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
The angle sum of the n-sided polygon is ( n – 2 ) * \(180^0\) = n * \(108^0\).
So, 72*n = \(360^0\) or n = 5.
Condition 1) is sufficient.

Condition 2)
If the length of each side is 24, then n = 120/24 = 5.
If the length of each side is 20, then n = 120/20 = 6.
Since we don’t have a unique solution, condition 2) is not sufficient.

Therefore, A is the answer.

Answer: A